Conquering the Integral of (1/x)*exp(-ax^2): A Scientific Inquiry

[GrandsonOfMagnusCarl]

Homework Statement

Essentially - find <1/x>, i.e. the mean of 1/x. The distribution probability density is of the form exp(-ax^2).

Relevant Equations

Mean of G = integrate ( G f(x) ) dx

Hopeless. I tried to use Taylor expansion but the zeroes and infinities go out of control really quick.
I tried WolframAlpha and it gave a special function.
What integrating trick am I missing? Or is it nonsense to solve it simply by hand?

 

[Orodruin]

The expectation value is infinite.

 

[GrandsonOfMagnusCarl]

The expectation value is infinite.

Ah I'm so stupid. Thank you. Also another reality check for me.

 

[Incorrect]

<1/x>=0 as 1/x is an odd function and G*f(x) is then also odd.